Question

The charge life of a certain lithium ion battery for camcorders is normally distributed, with mean 90 minutes and standard deviation 35 minutes.
(a) What is the probability that a randomly selected battery of this type lasts more than 100 minutes on a single charge? Is this result unusual?
(b) Describe the sampling distribution of x̄, the sample mean charge life for a random sample of 10 such batteries.
(c) What is the probability that a random sample of 10 such batteries has a mean charge life of more than 100 minutes? Is this result unusual?
(d) What is the probability that a random sample of 25 such batteries has a mean charge life of more than 100 minutes?
(e) Explain what causes the probabilities in parts (c) and (d) to be different.